public class BinTree {

    private int root;
    private BinTree left;
    private BinTree right;
    private boolean empty = false;

    public BinTree(int rt, BinTree l, BinTree r) {
        root = rt;
        left = l;
        right = r;
    }

    public BinTree() {
        empty = true;
    }

    public BinTree(double p) {
        if (Math.random() < p) {
            empty = true;
        } else {
            root = (int)(Math.random()*100);
            left = new BinTree(p*1.1);
            right = new BinTree(p*1.1);
        }
    }

    public boolean isEmpty() {
        return empty;
    }

    public int size() {
        if(isEmpty() == true) {
            return 0;
        } else {
            return left.size() + right.size() + 1;
        }
    }

    public int height() {
        if(isEmpty()) {
            return -1;
        } else {
            return 1 + Math.max(left.height(), right.height());
        }
    }

    public int leaves() {
        if (isEmpty()){
            return 0;
        }else if(height()==0){
            return 1;
        }else{
            return left.leaves() + right.leaves();
        }
    }

    public boolean search(int n) {
        if (isEmpty()){
            return false;
        }else{
            return root == n||left.search(n)||right.search(n);
        }
    }

    public void print() {
        if (!isEmpty()){
            left.print();
            right.print();
            System.out.println(root);

        }
    }

    public boolean perfect(){
        if(isEmpty()){
            return true;
        }else{
            return left.height() == right.height() &&
            left.perfect() && right.perfect();
        }
    }

}